You are correct that it is a common misconception that arm length has to be the same on both ends. It does not.

But I still maintain that if the holes of a 'classic' rudder horn are lined up with the hinge you will get slack with a round servo output disc like the one abuckner asks about. That wheel has a slot around the edge that holds the cable like a reel.

You can build a model of the round-wheel-to-arm setup to see the result or better yet use a drawing program that will show dimensions such as Corel or Visio.